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10.3 Professional Sports

10.3 Professional Sports
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  • 1. Calculating Batting Averages

    The 2010 hitting statistics of 10 Major League Baseball players are shown.

    Which player had the greatest batting average (AVG) in 2010? (See Example 1 and Example 2.)

    • Worked-Out Solution

      To find the batting average for a player, divide hits by at bats. The formula is

      Using a spreadsheet, you can calculate the batting average for each player.

       

      With a batting average of 0.359, Josh Hamilton had the greatest batting average among the players in the table. Incidentally, Josh Hamilton's batting average was also the greatest batting average of any player in Major League Baseball in 2010.

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      _____     _____     _  __     ___     __   __  
     / ____||  |  ___||  | |/ //   / _ \\   \ \\/ // 
    / //---`'  | ||__    | ' //   / //\ \\   \   //  
    \ \\___    | ||__    | . \\  |  ___  ||  / . \\  
     \_____||  |_____||  |_|\_\\ |_||  |_|| /_//\_\\ 
      `----`   `-----`   `-` --` `-`   `-`  `-`  --` 
                                                     
    
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  • 2. Calculating Slugging Percentage

    The 2010 hitting statistics of 10 Major League Baseball players are shown.

    Slugging percentage (SLG) is a statistic used to measure the power of a hitter. The formula to calculate slugging percentage is shown. Find the slugging percentage for each player. (See Example 1 and Example 2.)

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      ____       ___      _  _    __   __    _____   
     |  _ \\    / _ \\   | \| ||  \ \\/ //  |__  //  
     | |_| ||  / //\ \\  |  ' ||   \ ` //     / //   
     | .  //  |  ___  || | .  ||    | ||     / //__  
     |_|\_\\  |_||  |_|| |_|\_||    |_||    /_____|| 
     `-` --`  `-`   `-`  `-` -`     `-`'    `-----`  
                                                     
    
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  • 3. Calculating On-Base Percentages

    The 2010 hitting statistics of 10 Major League Baseball players are shown.

    On-base percentage (OBP) is a statistic used to measure how often a player reaches base. The formula to calculate on base percentage is shown. Find the on-base percentage for each player. (See Example 1 and Example 2.)

    • Worked-Out Solution

      Using a spreadsheet, you can calculate the on-base percentage for each player.

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     _    _    __   __    ______   __   __   _    _   
    | \  / ||  \ \\/ //  /_   _//  \ \\/ // | \  / || 
    |  \/  ||   \ ` //     | ||     \ ` //  |  \/  || 
    | .  . ||    | ||     _| ||      | ||   | .  . || 
    |_|\/|_||    |_||    /__//       |_||   |_|\/|_|| 
    `-`  `-`     `-`'    `--`        `-`'   `-`  `-`  
                                                      
    
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  • 4. Most Valuable Player

    The 2010 hitting statistics of 10 Major League Baseball players are shown.

    Considering AVG, SLG, and OBP, which player would you choose as the most valuable player (MVP)? Explain your reasoning. (See Examples 1 and Example 2.)

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      ______    ______    _____    _    _    _    _   
     /_____//  /_   _//  / ____|| | || | || | || | || 
     `____ `    -| ||-  / //---`' | || | || | || | || 
     /___//     _| ||_  \ \\___   | \\_/ || | \\_/ || 
     `__ `     /_____//  \_____||  \____//   \____//  
     /_//      `-----`    `----`    `---`     `---`   
     `-`                                              
    
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  • 5. On-Base Percentage Less than Batting Average

    The 2010 hitting statistics of 10 Major League Baseball players are shown.

    Is it possible for a player to have an on-base percentage that is less than his AVG? Explain your reasoning. (See Example 1 and Example 2.)

    • Worked-Out Solution

      Not only is it possible for a player to have an on-base percentage less than his batting average, it has actually happened. Consider for instance the following statistics for player Ernie Bowman from 1963.

      Sacrifice flies lower a player's on-base percentage. If a player has a high enough number of sacrifice flies, his on-base percentage can be less than his batting average.

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               _    _    _____     __   __    _____   
      ____    | || | || |  __ \\   \ \\/ //  / ____|| 
     |    \\  | || | || | |  \ ||   \ ` //  / //---`' 
     | [] ||  | \\_/ || | |__/ ||    | ||   \ \\___   
     |  __//   \____//  |_____//     |_||    \_____|| 
     |_|`-`     `---`    -----`      `-`'     `----`  
     `-`                                              
    
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  • 6. Stolen Base Percentage

    The 2010 hitting statistics of 10 Major League Baseball players are shown.

    Albert Pujols had a stolen base percentage (SB%) of 77.8%. Write a formula using abbreviations to calculate SB%. (See Examples 1 and Example 2.)

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     _    _    _    _     ______   __   __   _    _   
    | \  / || | || | ||  /_   _//  \ \\/ // | || | || 
    |  \/  || | || | ||    | ||     \ ` //  | || | || 
    | .  . || | \\_/ ||   _| ||      | ||   | \\_/ || 
    |_|\/|_||  \____//   /__//       |_||    \____//  
    `-`  `-`    `---`    `--`        `-`'     `---`   
                                                      
    
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